bandwidth {stats} | R Documentation |

## Bandwidth Selectors for Kernel Density Estimation

### Description

Bandwidth selectors for gaussian windows in `density`

.

### Usage

bw.nrd0(x)
bw.nrd(x)
bw.ucv(x, nb = 1000, lower = 0.1 * hmax, upper = hmax)
bw.bcv(x, nb = 1000, lower = 0.1 * hmax, upper = hmax)
bw.SJ(x, nb = 1000, lower = 0.1 * hmax, upper = hmax,
method = c("ste", "dpi"))

### Arguments

`x` |
A data vector. |

`nb` |
number of bins to use. |

`lower, upper` |
Range over which to minimize. The default is
almost always satisfactory. `hmax` is calculated internally
from a normal reference bandwidth. |

`method` |
Either `"ste"` ("solve-the-equation") or
`"dpi"` ("direct plug-in"). |

### Details

`bw.nrd0`

implements a rule-of-thumb for
choosing the bandwidth of a Gaussian kernel density estimator.
It defaults to 0.9 times the
minimum of the standard deviation and the interquartile range divided by
1.34 times the sample size to the negative one-fifth power
(= Silverman's “rule of thumb”, Silverman (1986, page 48, eqn (3.31))
*unless* the quartiles coincide when a positive result
will be guaranteed.

`bw.nrd`

is the more common variation given by Scott (1992),
using factor 1.06.

`bw.ucv`

and `bw.bcv`

implement unbiased and
biased cross-validation respectively.

`bw.SJ`

implements the methods of Sheather & Jones (1991)
to select the bandwidth using pilot estimation of derivatives.

### Value

A bandwidth on a scale suitable for the `bw`

argument
of `density`

.

### References

Scott, D. W. (1992)
*Multivariate Density Estimation: Theory, Practice, and
Visualization.*
Wiley.

Sheather, S. J. and Jones, M. C. (1991)
A reliable data-based bandwidth selection method for kernel density
estimation.
*Journal of the Royal Statistical Society series B*,
**53**, 683–690.

Silverman, B. W. (1986)
*Density Estimation*.
London: Chapman and Hall.

Venables, W. N. and Ripley, B. D. (2002)
*Modern Applied Statistics with S*.
Springer.

### See Also

`density`

.

`bandwidth.nrd`

, `ucv`

,
`bcv`

and `width.SJ`

in
package **MASS**, which are all scaled to the `width`

argument
of `density`

and so give answers four times as large.

### Examples

plot(density(precip, n = 1000))
rug(precip)
lines(density(precip, bw="nrd"), col = 2)
lines(density(precip, bw="ucv"), col = 3)
lines(density(precip, bw="bcv"), col = 4)
lines(density(precip, bw="SJ-ste"), col = 5)
lines(density(precip, bw="SJ-dpi"), col = 6)
legend(55, 0.035,
legend = c("nrd0", "nrd", "ucv", "bcv", "SJ-ste", "SJ-dpi"),
col = 1:6, lty = 1)

[Package

*stats* version 2.5.0

Index]